Michael Jordan’s book.. Considering how the ending of the book was written, is it an effective ending? Did the ending surprise you? Why? Why not? Did the ending leave you with unanswered questions? Explain.

Watch the video below, and then answer the questions below. http://www.youtube.com/watch?v=tZbDMUaqwE8 What does J.D. Bowen say is the problem with realism? A. Realism places too much emphasis on security, and thus its answers are all about conflict. B. Realism is too deterministic, ignoring the unpredictable human element in international relations. C. Realism discounts the possibility of progress and positive change. D. Realism can’t explain why a small country would fight a larger, more powerful one. E. Realism is like liberalism without a moral compass. Which of the following is NOT a characteristic of liberal thought? A. There are important issues in international relations beyond security and conflict. B. International actors have opportunities for cooperation. C. There is no real conflict of interests in international politics. D. Businesses and other non-state organizations have power. E. Interdependence is a facet of the international system. According to liberal theory, which of the following would be a potential actor in the international political system? A. states B. businesses C. aid groups D. churches E. all of these options Bowen claims that the United Nations is based on a “clearly liberal logic.” What is that logic? A. preventing conflict through the efforts of non-state actors B. preventing conflict through collective security C. preventing conflict through nuclear deterrence D. promoting freedom and democracy E. holding Germany accountable for its aggression in World War II Which of the following would most likely be a research topic for liberal theorists? A. how cultures develop identities B. how states can measure their military power by counting equipment and personnel C. how the United Nations can be more effective at preventing war D. why security is a masculine concept E. all of these options ———————————————————————————————————————

Chapter 14 Practice Problems (Practice – no credit) Due: 11:59pm on Friday, May 16, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Harmonic Oscillator Equations Learning Goal: To derive the formulas for the major characteristics of motion as functions of time for a horizontal spring oscillator and to practice using the obtained formulas by answering some basic questions. A block of mass is attached to a spring whose spring constant is . The other end of the spring is fixed so that when the spring is unstretched, the mass is located at . . Assume that the +x direction is to the right. The mass is now pulled to the right a distance beyond the equilibrium position and released, at time , with zero initial velocity. Assume that the vertical forces acting on the block balance each other and that the tension of the spring is, in effect, the only force affecting the motion of the block. Therefore, the system will undergo simple harmonic motion. For such a system, the equation of motion is , and its solution, which provides the equation for , is . Part A At what time does the block come back to its original equilibrium position ( ) for the first time? Express your answer in terms of some or all of the variables: , , and . You did not open hints for this part. ANSWER: m k x = 0 A t = 0 a(t) = − x(t) km x(t) x(t) = Acos( t) km −− t1 x = 0 A k m Part B Find the velocity of the block as a function of time. Express your answer in terms of some or all of the variables: , , , and . You did not open hints for this part. ANSWER: Part C This question will be shown after you complete previous question(s). t1 = v k m A t v(t) = Typesetting math: 100% Part D Find the acceleration of the block as a function of time. Express your answer in terms of some of all of the variables: , , , and . ANSWER: Part E Specify when the magnitude of the acceleration of the block reaches its maximum value. Consider the following options: only once during one a. period of motion, b. when the block’s speed is zero, c. when the block is in the equilibrium position, d. when the block’s displacement equals either or , e. when the block’s speed is at a maximum. Choose the most complete answer. You did not open hints for this part. ANSWER: a k m A t a(t) = A −A Typesetting math: 100% Part F Find the kinetic energy of the block as a function of time. Express your answer in terms of some or all of the variables: , , , and . You did not open hints for this part. ANSWER: Part G Find , the maximum kinetic energy of the block. Express your answer in terms of some or all of the variables: , , and . ANSWER: a only b only c only d only e only b and d c and e b and c a and e d and e K k m A t K(t) = Kmax k m A Typesetting math: 100% Part H The kinetic energy of the block reaches its maximum when which of the following occurs? You did not open hints for this part. ANSWER: Mass and Simple Harmonic Motion Conceptual Question The shaker cart, shown in the figure, is the latest extreme sport craze. You stand inside of a small cart attached to a heavy-duty spring, the spring is compressed and released, and you shake back and forth, attempting to maintain your balance. Note that there is also a sandbag in the cart with you. Kmax = The displacement of the block is zero. The displacement of the block is . The acceleration of the block is at a maximum. The velocity of the block is zero. A Typesetting math: 100% At the instant you pass through the equilibrium position of the spring, you drop the sandbag out of the cart onto the ground. Part A What effect does dropping the sandbag out of the cart at the equilibrium position have on the amplitude of your oscillation? You did not open hints for this part. ANSWER: Part B This question will be shown after you complete previous question(s). Instead of dropping the sandbag as you pass through equilibrium, you decide to drop the sandbag when the cart is at its maximum distance from equilibrium. Part C This question will be shown after you complete previous question(s). Part D It increases the amplitude. It decreases the amplitude. It has no effect on the amplitude. Typesetting math: 100% This question will be shown after you complete previous question(s). Simple Harmonic Motion Conceptual Question An object of mass is attached to a vertically oriented spring. The object is pulled a short distance below its equilibrium position and released from rest. Set the origin of the coordinate system at the equilibrium position of the object and choose upward as the positive direction. Assume air resistance is so small that it can be ignored. Refer to these graphs when answering the following questions. Part A Beginning the instant the object is released, select the graph that best matches the position vs. time graph for the object. You did not open hints for this part. ANSWER: m Typesetting math: 100% Part B Beginning the instant the object is released, select the graph that best matches the velocity vs. time graph for the object. You did not open hints for this part. ANSWER: Part C Beginning the instant the object is released, select the graph that best matches the acceleration vs. time graph for the object. A B C D E F G H A B C D E F G H Typesetting math: 100% You did not open hints for this part. ANSWER: Harmonic Oscillator Acceleration Learning Goal: To understand the application of the general harmonic equation to finding the acceleration of a spring oscillator as a function of time. One end of a spring with spring constant is attached to the wall. The other end is attached to a block of mass . The block rests on a frictionless horizontal surface. The equilibrium position of the left side of the block is defined to be . The length of the relaxed spring is . The block is slowly pulled from its equilibrium position to some position along the x axis. At time , the block is released with zero initial velocity. The goal of this problem is to determine the acceleration of the block as a function of time in terms of , , and . It is known that a general solution for the position of a harmonic oscillator is , where , , and are constants. Your task, therefore, is to determine the values of , , and in terms of , ,and and then use the connection between and to find the acceleration. A B C D E F G H k m x = 0 L xinit > 0 t = 0 a(t) k m xinit x(t) = C cos (t) + S sin (t) C S C S k m xinit x(t) a(t) Typesetting math: 100% Part A Combine Newton’s 2nd law and Hooke’s law for a spring to find the acceleration of the block as a function of time. Express your answer in terms of , , and the coordinate of the block . You did not open hints for this part. ANSWER: Part B This question will be shown after you complete previous question(s). Part C a(t) k m x(t) a(t) = Typesetting math: 100% This question will be shown after you complete previous question(s). ± Introduction to Simple Harmonic Motion Consider the system shown in the figure. It consists of a block of mass attached to a spring of negligible mass and force constant . The block is free to move on a frictionless horizontal surface, while the left end of the spring is held fixed. When the spring is neither compressed nor stretched, the block is in equilibrium. If the spring is stretched, the block is displaced to the right and when it is released, a force acts on it to pull it back toward equilibrium. By the time the block has returned to the equilibrium position, it has picked up some kinetic energy, so it overshoots, stopping somewhere on the other side, where it is again pulled back toward equilibrium. As a result, the block moves back and forth from one side of the equilibrium position to the other, undergoing oscillations. Since we are ignoring friction (a good approximation to many cases), the mechanical energy of the system is conserved and the oscillations repeat themselves over and over. The motion that we have just described is typical of most systems when they are displaced from equilibrium and experience a restoring force that tends to bring them back to their equilibrium position. The resulting oscillations take the name of periodic motion. An important example of periodic motion is simple harmonic motion (SHM) and we will use the mass-spring system described here to introduce some of its properties. Part A Which of the following statements best describes the characteristic of the restoring force in the spring-mass system described in the introduction? You did not open hints for this part. ANSWER: m k The restoring force is constant. The restoring force is directly proportional to the displacement of the block. The restoring force is proportional to the mass of the block. The restoring force is maximum when the block is in the equilibrium position. Typesetting math: 100% Part B As shown in the figure, a coordinate system with the origin at the equilibrium position is chosen so that the x coordinate represents the displacement from the equilibrium position. (The positive direction is to the right.) What is the initial acceleration of the block, , when the block is released at a distance from its equilibrium position? Express your answer in terms of some or all of the variables , , and . You did not open hints for this part. ANSWER: Part C What is the acceleration of the block when it passes through its equilibrium position? Express your answer in terms of some or all of the variables , , and . You did not open hints for this part. ANSWER: a0 A A m k a0 = a1 A m k Typesetting math: 100% Part D This question will be shown after you complete previous question(s). Using the information found so far, select the correct phrases to complete the following statements. Part E You did not open hints for this part. ANSWER: Part F You did not open hints for this part. ANSWER: a1 = The magnitude of the block’s acceleration reaches its maximum value when the block is in the equilibrium position. at either its rightmost or leftmost position. between its rightmost position and the equilibrium position. between its leftmost position and the equilibrium position. Typesetting math: 100% Part G You did not open hints for this part. ANSWER: Part H Because of the periodic properties of SHM, the mathematical equations that describe this motion involve sine and cosine functions. For example, if the block is released at a distance from its equilibrium position, its displacement varies with time according to the equation , where is a constant characteristic of the system. If time is measured is seconds, must be expressed in radians per second so that the quantity is expressed in radians. Use this equation and the information you now have on the acceleration and speed of the block as it moves back and forth from one side of its equilibrium position to the other to determine the correct set of equations for the block’s x components of velocity and acceleration, and , respectively. In the expressions below, and are nonzero positive constants. You did not open hints for this part. The speed of the block is zero when it is in the equilibrium position. at either its rightmost or leftmost position. between its rightmost position and the equilibrium position. between its leftmost position and the equilibrium position. The speed of the block reaches its maximum value when the block is in the equilibrium position. at either its rightmost or leftmost position. between the rightmost position and the equilibrium position. between the leftmost position and the equilibrium position. A x t x = Acost t vx ax B C Typesetting math: 100% ANSWER: Period of a Pendulum Ranking Task Part A Six pendulums of mass and length as shown are released from rest at the same angle from vertical. Rank the pendulums according to the number of complete cycles of motion each pendulum goes through per minute. Rank from most to least complete cycles of motion per minute. To rank items as equivalent, overlap them. You did not open hints for this part. ANSWER: , , , , vx = −Bsint ax = C cost vx = Bcost ax = C sint vx = −Bcost ax = −C cost vx = −Bsint ax = −C cost m L Typesetting math: 100% ± Gravity on Another Planet After landing on an unfamiliar planet, a space explorer constructs a simple pendulum of length 47.0 . The explorer finds that the pendulum completes 108 full swing cycles in a time of 138 . Part A What is the magnitude of the gravitational acceleration on this planet? Express your answer in meters per second per second. You did not open hints for this part. cm s Typesetting math: 100% ANSWER: ± Tactics Box 14.1 Identifying and Analyzing Simple Harmonic Motion Learning Goal: To practice Tactics Box 14.1 Identifying and analyzing simple harmonic motion. A complete description of simple harmonic motion must take into account several physical quantities and various mathematical relations among them. This Tactics Box summarizes the essential information needed to solve oscillation problems of this type. TACTICS BOX 14.1 Identifying and analyzing simple harmonic motion If the net force acting on a particle is a linear restoring force, the motion will be simple harmonic motion around the equilibrium 1. position. The position as a function of time is . The velocity as a function of time is . The maximum speed is . The equations are given here in terms of , but they can be written in terms of , or some other parameter if the situation calls for it. 2. 3. The amplitude and the phase constant are determined by the initial conditions through and . 4. The angular frequency (and hence the period ) depends on the physical properties of the situtaion. But does not depend on or . Mechanical energy is conserved. Thus .Energy conservation provides a relationship between position and velocity that is independent of time. 5. Part A The position of a 60 oscillating mass is given by , where is in seconds. Determine the velocity at . Express your answer in meters per second to two significant figures. You did not open hints for this part. ANSWER: gplanet = m/s2 x(t) = Acos(t + 0 ) vx(t) = −Asin(t + 0 ) vmax = A x y A 0 x0 = Acos 0 v0x = −Asin 0 T = 2/ A 0 1 m + k = k = m( 2 v2 x 1 2 x2 1 2 A2 1 2 vmax)2 g x(t) = (2.0 cm) cos(10t) t t = 0.40 s Typesetting math: 100% Part B Assume that the oscillating mass described in Part A is attached to a spring. What would the spring constant of this spring be? Express your answer in newtons per meter to two significant figures. You did not open hints for this part. ANSWER: Part C What is the total energy of the mass described in the previous parts? Express your answer in joules to two significant figures. You did not open hints for this part. ANSWER: Score Summary: Your score on this assignment is 0%. You received 0 out of a possible total of 0 points. vx = m/s k k = N/m E E = J Typesetting math: 100%

Chapter 05 Homework Due: 11:59pm on Friday, May 23, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Activity: Human Population Growth Click here to complete this activity. Then answer the questions. Part A Which of these was the first of the major events that stimulated an increase in the size of the human population? ANSWER: Correct The advent of agriculture is the first of the events listed here that stimulated an increase in the size of the human population. Part B Which of these was the second of the major events that stimulated an increase in the size of the human population? ANSWER: Correct The Industrial Revolution was the second of the major events that stimulated an increase in the size of the human population. Part C Which of these was the third of the major events that stimulated an increase in the size of the human population? ANSWER: Correct The advent of modern medicine is the third and most recent of the events listed here that have stimulated an increase in the population size of humans. the Industrial Revolution the advent of agriculture the discovery of antibiotics the bubonic plague the discovery of vaccines the discovery of vaccines the discovery of antibiotics the advent of agriculture the Industrial Revolution the bubonic plague the discovery of vaccines the advent of agriculture the discovery of antibiotics the discovery of vaccines and the discovery of antibiotics the Industrial Revolution Chapter 05 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 1 of 8 5/21/2014 8:00 PM Part D Currently, how large is the worldwide population of humans relative to Earth’s carrying capacity for humans? ANSWER: Correct Not knowing how technological innovations will affect the human population means there is insufficient information to answer this question. Activity: Analyzing Age-Structure Pyramids Click here to complete this activity. Then answer the questions. Part A Ignoring migration, the age structure of a human population likely to increase in size will have what shape? ANSWER: Correct This would mean that most individuals are in the prereproductive years. Such a population is expected to increase. Part B Ignoring migration, the age structure of a human population likely to decrease in size will have what shape? ANSWER: Correct In such a population the majority of individuals are in their postreproductive years. Such a population is expected to decrease. Part C Ignoring migration, the age structure diagram of a human population likely to maintain a relatively stable size will have what shape? There is insufficient information to answer this question. either at or above the carrying capacity below the carrying capacity above the carrying capacity at the carrying capacity Both an inverted pyramid and a rectangle tapering toward the top result in a population that increases in size. pyramid Both a pyramid and a rectangle tapering toward the top result in a population that increases in size. a rectangle tapering toward the top inverted pyramid pyramid Both an inverted pyramid and a rectangle tapering toward the top result in a population that decreases in size. Both a pyramid and a rectangle tapering toward the top result in a population that decreases in size. a rectangle tapering toward the top inverted pyramid Chapter 05 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 2 of 8 5/21/2014 8:00 PM ANSWER: Correct Such a population is expected to have a relatively stable size. GraphIt!: Age Pyramids and Population Growth Click here to complete the graphing activity. Then answer the questions. Part A – Question 1 The population of Greece is expected to _______. Hint 1. Review Step 2 of this activity. What shape does this population have? ANSWER: Correct Part B – Question 2 Assuming the current trend continues, in 30 years Greece will have more children than reproductive-age individuals. Hint 1. What age group will today’s newborns occupy in 2030? ANSWER: Correct Part C – Question 3 Assuming the current trend continues, in 30 years Greece will have more children than elderly members of the population. Hint 1. Both an inverted pyramid and a rectangle tapering toward the top result in a population that remains stable in size. pyramid Both a pyramid and a rectangle tapering toward the top result in a population that remains stable in size. inverted pyramid a rectangle tapering toward the top expand remain stable decline True False Chapter 05 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 3 of 8 5/21/2014 8:00 PM What age groups will today’s reproductive-age individuals occupy in 2030? ANSWER: Correct Part D – Question 4 Assuming the current trend continues, in 30 years Greece will have more reproductive-age individuals than children. ANSWER: Correct Part E – Question 5 Assuming the current trend continues, in 30 years Greece will have more elderly than reproductive-age individuals. ANSWER: Correct Part F – Question 6 Greece had more females than males in 2000. Which of the following is the most likely explanation for this? Hint 1. Which sex tends to live longer in the United States, males or females? ANSWER: Correct Part G – Question 7 The population of Colombia is currently _______. Hint 1. Review Step 2 of this activity. What shape does this population have? ANSWER: True False True False True False Females generally have a shorter life span than males. More females are born than males, and this difference remains throughout all age groups. There should be an equal number of males and females in every age group, so this is likely an error in the 2000 census for Greece. Males generally have a shorter life span than females. expanding stable declining Chapter 05 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 4 of 8 5/21/2014 8:00 PM Correct Part H – Question 8 Assuming the current trend continues, in 30 years Colombia will have more children than reproductive-age individuals. Hint 1. What age group will today’s newborns occupy in 2030? ANSWER: Correct Part I – Question 9 Assuming the current trend continues, in 30 years Colombia will have more children than elderly members of the population. Hint 1. What age groups will today’s reproductive-age individuals occupy in 2030? ANSWER: Correct Part J – Question 10 Assuming the current trend continues, in 30 years Colombia will have more reproductive-age individuals than children. ANSWER: Correct Part K – Question 11 Assuming the current trend continues, in 30 years Colombia will have more elderly than reproductive-age individuals. ANSWER: Correct Concept Review: Demographic Transition Model Can you identify what happens in each stage of the demographic transition model? Part A Drag the labels to the appropriate targets. ANSWER: True False True False True False True False Chapter 05 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 5 of 8 5/21/2014 8:00 PM Answer Requested Concept Review: Demographic Characteristics of Developed and Developing Nations For each demographic characteristic described in the table below, decide whether it applies to developed nations, developing nations, or neither group. Part A Drag the correct labels onto the table. Labels may be used once, more than once, or not at all. ANSWER: Concept Review: Age Structure Diagrams Chapter 05 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 6 of 8 5/21/2014 8:00 PM Can you label age structure diagrams? Part A Drag the labels to the appropriate targets. Pink labels indicate what each age class represents. Blue labels indicate how the population is expected to change over time. ANSWER: Correct Current Events: Nigeria Tested by Rapid Rise in Population (New York Times, 4/14/2012) Read this New York Times article and then answer the questions. Nigeria Tested by Rapid Rise in Population (4/14/2012) Registration with The New York Times provides instant access to breaking news on NYTimes.com. To register, go to http://www.nytimes.com/register. Visit http://www.nytimes.com /content/help/rights/terms/terms-of-service.html to review the current NYT Terms of Service. Part A The current human population is just over _______ billion people. ANSWER: Correct Part B How are the governments of sub-Saharan Africa reacting to a rapidly increasing population? ANSWER: Part C Which of the following tends to be true? ANSWER: 6 7 8 9 They are beginning to encourage people to have fewer children. They are doing nothing. They are waiting to hear the recommendations from the United Nations. They are still encouraging people to have many children. Chapter 05 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 7 of 8 5/21/2014 8:00 PM Part D You are in the Nigerian government and are working on trying to solve the problem of a rapidly increasing population. You decide to incorporate the Latin American model as part of your plan. Which of the following do you recommend? ANSWER: Part E If nearly every adult in a society is married and polygamy is common, which of the following is true? ANSWER: Part F Even if global total fertility rate drops to 2.1, estimates indicate that the human population will reach ________ by 2100. ANSWER: Score Summary: Your score on this assignment is 57.9%. You received 15.06 out of a possible total of 26 points. The relationship between changing population and unemployment rates is too variable to quantify. An increase in population leads to an increase in unemployment. Population growth and unemployment are not correlated. An increase in population leads to a decrease in unemployment. There will be tax breaks for families with fewer children. Girls will be required to finish high school. The government will impose a limit of only one child. The government will provide free family planning. There are more adult women than adult men. There are equal numbers of adult men and adult women. There are more adult men than adult women. The ratio of adult men to adult women would depend on the total fertility rate. 10 billion 12 billion 14 billion 16 billion Chapter 05 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 8 of 8 5/21/2014 8:00 PM

Physics 2010 Sid Rudolph Fall 2009 MIDTERM 4 REVIEW Problems marked with an asterisk (*) are for the final. Solutions are on the course web page. 1. A. The drawing to the right shows glass tubing, a rubber bulb and two bottles. Is the situation you see possible? If so, carefully describe what has taken place in order to produce the situation depicted. B. The picture depicts three glass vessels, each filled with a liquid. The liquids each have different densities, and DA > DB > DC. In vessel B sits an unknown block halfway to the bottom and completely submerged. 1. _______ In which vessel would the block sit on the bottom? 2. _______ In which vessel would the block float on the top? 3. _______ In which vessel would the block feel the smallest buoyant force? 4. _______ In which vessels are buoyant forces on the block are the same? 5. _______ Assume the coefficient of volume expansion for the liquid in B and the block are $B > $block. If the temperature of vessel B with the block is raised, would block B rise to the surface, sink to the bottom, or remain where it is? 2. A circular tank with a 1.50 m radius is filled with two fluids, a 4.00 m layer of water and a 3.00 m layer of oil. Use Doil = 8.24 × 10 kg/m and Dwater = 1.00 × 10 kg/m , and Datm = 1.01 × 10 N/m . 2 3 3 3 5 2 A. What are the gauge and absolute pressures 1.00 m above the bottom of the tank? B. A block of material in the shape of a cube (m = 100 kg and side length = 42.0 cm) is released at the top of the oil layer. Where does the block come to rest? Justify your answer. If it comes to rest between two layers, specify which layers and what portion of the block sits in each layer. [Note: Vcube = a ]3 C. A small 1.00 cm radius opening is made in the side of the tank 0.500 m up from its base (block was removed). What volume of water drains from the tank in 10.0 s? (b) (a) 3. A tube is inserted into a vein in the wrist of a patient in a reclined position on a hospital bed. The heart is vertically 25.0 cm above the position of the wrist where the tube is inserted. Take DBLOOD = 1.06 × 103 kg/m3. The gauge venous blood pressure at the level of the heart is 6.16 × 103 N/m2. Assume blood behaves as an ideal nonviscous fluid. A. What is the gauge venous blood pressure at the position of the wrist? B. The tube coming from the wrist is connected to a bottle of whole blood the patient needs in a transfusion. See above figure (b). What is the minimum height above the level of the heart at which the bottle must be held to deliver the blood to the patient? C. Suppose the bottle of blood is held 1.00 m above the level of the heart. Assume the tube inserted in the wrist has a diameter of 2.80 mm. What is the velocity, v, and flow rate of blood as it enters the wrist. You may also assume the rate at which the blood level in the bottle drops is very small. The answer you get here is a substantial overstatement. Blood is not really a non-viscous fluid. 4. A 0.500 kg block is attached to a horizontal spring and oscillates back and forth on a frictionless surface with a frequency of f = 3.00 hz. The amplitude of this motion is 6.00 × 10 m. Assume to = 0 and is the instant the block is -2 at the equilibrium position moving to the left. A. Write expressions x(t) = !A sin (Tt) and v(t) = !AT cos (Tt) filling in the values of A and T. B. What is the total mechanical energy (METOT) of the block-spring system? C. Suppose the block, at the moment it reaches its maximum velocity to the left splits in half with only one of the halves remaining attached to the spring. What are the amplitude and frequency of the resulting oscillations? D. Suppose, instead of splitting at the position of maximum velocity to the left, the block now splits when it is at the extreme position in the left. What are the amplitude and frequency of the resulting motion? E. Describe in words what would happen to the period of oscillation if a second block identical to the first block were dropped on the first block at either of its extreme positions. 5. A. A spring has one end attached to a wall and the other end attached to two identical masses, mA and mB. The system is set into oscillation on a frictionless surface with amplitude A. See figure. When the system is momentarily at rest at x = -A whatever it is that holds mA to mB fails; and later in the motion mB moves away from mA to the right. 1. Location where the acceleration of mA is maximum and negative. 2. Location where the KE of mA is maximum. The next few questions ask you to compare the behavior of the mass-spring system after and before mB detached. Energy considerations are most useful here. 3. The amplitude of the mass-spring oscillation has (increased, decreased, not changed) after mB detaches. 4. The frequency of the mass-spring oscillation has (increased, decreased, stayed the same) after mB detaches. 5. The maximum speed of mA has (increased, decreased, stayed the same) after mB detaches. 6. The period of oscillation of the mass-spring system has (increased, decreased, stayed the same) after mB detaches. 7. The fraction of the total mechanical energy of the entire spring-2 mass system carried away with mB after mB detaches is B. A spherical object is completely immersed in a liquid and is neutrally buoyant some distance above the bottom of the vessel. See figure. The upper surface of the liquid is open to the earth’s atmosphere. 1. How is the density of the fluid related to the density of the spherical object? 2. Assume the fluid and object are incompressible. In addition, the $sphere (coefficient of volume expansion) > $liquid. For the following items below, indicate whether the object sinks to the bottom, rises to the surface, or does nothing based on the changes described. a. Atmospheric pressure drops by 20%. b. Salt is dissolved in the liquid in the same way fresh water is turned into salt water. c. The entire apparatus is warmed 10oC (liquid and object are both warmed). d. The entire apparatus is transported to the surface of the moon. (gmoon = 1.6 m/s , PATM = 0 on moon) 2 e. 100 cm3 of the liquid is removed from the top. The object is still initially submerged. 6. A. A mass m is attached to a spring and oscillating on a frictionless, horizontal surface. See figure. At the instant the mass passes the equilibrium position moving to the right, half the mass detaches from the other half. The oscillating system is now the spring and half the original mass with the detached mass moving off to the right with constant velocity. Relative to the original spring-mass system, the new spring-mass system with half the mass oscillates with … In the spaces provided below, enter the words larger, smaller or the same that best completes the above sentence.. 1. amplitude 2. period 3. frequency 4. maximum velocity 5. mechanical energy B. A solid cylinder is floating at the interface between water and oil with 3/4 of the cylinder in the water region and 1/4 of the cylinder in the oil region. See figure. Select the item in the parenthesis that best fits the statement. 1. The item (oil, water, and/or cylinder) with the largest density. 2. The item (oil, water, and/or cylinder) with the smallest density. 3. The weight of the cylinder (is equal to, greater than or less than) the total buoyant force it feels. 4. The density of the cylinder (is equal to, less than, or greater than) the density of water. rC. Three thermometers in different settings record temperatures T1 = 1000°F, T2 = 1000°C, and T3 = 1000 K. In the space below select T1, T2 or T3, that best fits the statement. 1. The thermometer in the hottest environment. 2. The thermometer in the coolest environment. 3. The thermometer reading a temperature 900° above the boiling point of water. 7. An oil tanker in the shape of a rectangular solid is filled with oil (Doil = 880 kg/m ). The flat bottom of the 3 hull is 48.0 m wide and sits 26.0 m below the surface of the surrounding water. Inside the hull the oil is stored to a depth of 24.0 m. The length of the tanker, assumed filled with oil along the entire length, is 280 m. View from Rear View from Side Note: Dsalt water = 1.015 × 10 kg/m ; Vrectangular solid = length × width × height. 3 3 A. At the bottom of the hull, what is the water pressure on the outside and the oil pressure on the inside of the horizontal bottom part of the hull? Assume the Po above the oil is the same as the Po above the water and its value is Po = 1.01 × 10 N/m . 5 2 B. If you did part A correctly you determined that the water pressure on the horizontal bottom part of the hull is larger than the oil pressure there. Explain why this MUST be the case. C. What buoyant force does the tanker feel? D. What is the weight of the tanker, excluding the weight of the oil in the hull? 8. A. Water is poured into a tall glass cylinder until it reaches a height of 24.0 cm above the bottom of the cylinder. Next, olive oil (Doil = 920 kg/m ) is very carefully added until the total amount of 3 fluid reaches 48.0 cm above the bottom of the cylinder. Olive oil and water do not mix. See figure. Take Dwater = 1.00 × 10 kg/m and Patm = 1.01 × 10 N/m . 3 3 5 2 1. Indicate on the drawing which layer is water and which is olive oil. 2. What is the gauge pressure 10.0 cm below the top of the upper fluid layer in the cylinder. 3. What is the gauge pressure on the bottom of the cylinder? 4. If the cylinder is in the shape of a right circular cylinder with radius of 3.60 cm, what force is exerted on the bottom of the cylinder? B. A 0.200 kg mass is hung from a massless spring. At equilibrium, the spring stretched 28.0 cm below its unstretched length. This mass is now replaced with a 0.500 kg mass. The 0.500 kg mass is lowered to the original equilibrium position of the 0.200 kg mass and suddenly released producing vertical SHM. 1. What is the spring constant for this spring? 2. What is the period of oscillation for the 0.500 kg/spring system? 3. What is the amplitude of this oscillation? r9. The drawing shows a possible design for a thermostat. It consists of an aluminum rod whose length is 5.00 cm at 20.0°C. The thermostat switches an air conditioner when the end of the rod just touches the contact. The position of the contact can be changed with an adjustment screw. What is the size of the spacing such that the air conditioner turns on at 27.0°C. This is not a very practical device. Take “al = 2.3 × 10 /°C. -5 r10. The following is an effective technique for determining the temperature TF inside a furnace. Inside the furnace is 100 gm of molten (i.e., in a liquid state) lead (Pb). The lead is dropped into an aluminum calorimeter containing 200 gm water both at an initial temperature of 10.0°C. After equilibrium is reached, the temperature reads 21.8°C. Assumptions: (1) No water is vaporized; (2) no heat is lost to or gained from the environment; and (3) the specific heat for the lead is the same whether the lead is a solid or a liquid. DATA TABLE LEAD CALORIMETER WATER mPb = 100 gm mAl = 150 gm mW = 200 gm CPb = 0.0305 cal/gm°C CAl = 0.215 cal/gm°C CW = 1.0 cal/gm°C LF = 6.0 ca./gm (heat of fusion) Tinit = 10.0°C Tinit = 10.0°C MPPb = 327°C (melting point) TF = unknown Tequilibrium = 21.8°C A. In words, describe the distinct steps in the cooling of lead. B. How many calories of heat are absorbed by the calorimeter and the water it contains to reach 21.8°C? C. How many calories are lost by the lead in cooling from TF to the final equilibrium temperature of 21.8°C? D. What was the original furnace temperature? E. If the same amount of aluminum (CAl = 0.215 cal/gm°C and LM = 21.5 cal/gm) were used in the same furnace instead of lead, would the final equilibrium temperature be higher, less or the same as in the lead case? No calculation is needed to answer this. Please explain. r11. The length of aluminum cable between consecutive support towers carrying electricity to a large metropolitan area is 180.00 m on a hot August day when the temperature is 38°C. Use “(Al) = 24 × 10-6/°C. A. What is the length of the same section of aluminum cable on a very cold winter day when T = -24°C? B. If the same length of copper (” = 17 × 10-6/°C) cable (i.e., 180.00 m on the same hot August day) were used instead of aluminum, would the length of the copper cable be shorter, longer or the same as that of the aluminum on the same winter day as in (A)? Please explain your conclusion You do not have to do any calculations here. r12. You wish to make a cup of coffee with cream in a 0.250 kg mug (cmug = 900 J/kg°C) with 0.325 kg coffee (ccoffee = 4.18 × 10 J/kg°C) starting at 25.0°C and 0.010 kg cream (ccream = 3.80 × 10 J/kg°C) at 10.0°C. 3 3 You use a 50.0 W electric heater to bring the coffee, cream and mug to a final temperature of 90.0°C. How long must the coffee system be heated? Indicate clearly the assumptions you need to make. r13. A 75.0 kg patient is running a fever of 106°F and is given an alcohol rubdown to lower his body temperature. Take the specific heat of the human body to be Cbody = 3.48 × 10 J/kg°C, the heat of 3 evaporation of the rubbing alcohol to be Lv(alcohol) = 8.51 × 10 J/kg, and the density of the rubbing 5 alcohol to be 793 kg/m3. You may assume that all the heat removed from the fevered body goes into evaporating the alcohol, and that while the patient’s body is cooling, his metabolism adds no measurable heat. A. What quantity of heat must be removed from the body to lower its temperature to 99.0°F? B. What volume of rubbing alcohol is required? C. This is a qualitative question. Give an answer and explanation. Suppose you were told that the alcohol applied started at room temperature (. 70°F) and were given the specific heat for the alcohol. Thus, you now expect some of the body heat warming the alcohol to the temperature of the fever before evaporation occurs. How would this effect the result of the calculation in part (B)? r14. A 56.0 kg hypothermia victim is running a body temperature of 91.0°F. The victim is far away from any immediate medical treatment. Her friends decide to treat the hypothermia victim by placing the victim in a sleeping bag with one of her friends and use the heat from the friend to raise the victim’s body temperature. Take the specific heat of the human body to be Cbody = 3.48 × 10 J/kg°C. Assume that the sleeping bag acts 3 like a perfect calorimeter and also assume no heat is lost to or obtained from the sleeping bag. Finally, assume all the heat that warms the hypothermia victim comes from the basic metabolic heat produced by the body of the victim’s friend in the sleeping bag with her and that metabolism is rated at 2.00 × 106 cal/day, and that the victim’s metabolism is negligible. A. How much heat must be added to the victim’s body to get her temperature up to 98.0°F? B. How long must the victim remain in the sleeping bag with her friend to achieve this temperature change? C. This is a qualitative question. If the thermal characteristics of the sleeping bag are now taken into account, but still assuming no heat leaves or enters the sleeping bag, how will the answer to question (b) above be different? r15. A few years back a lawsuit was filed by a woman against McDonald’s because she scalded herself with a Styrofoam cup filled with coffee which she spilled on herself while driving. This question was spawned by that incredible legal action and represents a possible action taken by McDonald’s to insure cooler coffee. Suppose a typical cup of coffee sold by McDonald’s is basically 400 ml of hot water and when poured into the Styrofoam cup its temperature is 96.0°C. Take 1.00 ml to have a mass of 1.00 gm and = 4.19 kJ/kg°C. Neglect any heat lost to the cup and assume no heat is lost by the coffee to the environment. A. How much heat in joules must the coffee lose to bring its temperature to a drinkable 68.0°C? B. McDonald’s possible approach to lowering the temperature of the 96.0°C coffee to 68.0°C is to add a cube of ice initially at 0.0°C. (Take Lf = 334 kJ/kg.) What mass of ice has to be added to the coffee to reduce its initial temperature to the desired 68.0°C? r16. During this past Thanksgiving your instructor overdid it and consumed 3000 Cal of food and dessert. Remember 1.0 Cal = 4.19 x 10 J. For the questions below, as 3 sume no heat is lost to the environment. [Note: = 33.5 x 105 J/kg; = 4.19 x 103 J/kgoC] A. If all of this energy went into heating 65.0 kg water starting at 37.0oC (a mass approximately that of your instructor), what would be the final temperature of this water? B. Assume your instructor removes these overeating calories by running 10 kilometer races [note: 1.61 km = 1.00 mile]. Using the rule of thumb that 1 mile of jogging will require 100 Cal, what is the minimum number of races your instructor must run to consume the 3000 Cal in part A as exercise? C. The year before, your instructor was particularly gluttonous and consumed 5000 Cal. Assuming the same conditions of water mass (65.0 kg) and starting temperature (37.0oC) as in A, what is the final temperature of the water system, and if any water vaporizes to steam, how much? [Note: BP(H2O) = 100 C] o 17. Below is the position vs. time graph for the simple harmonic of a spring oscillation on a frictionless horizontal surface. Motion to the right is positive. 1. The earliest instant of time, including t0 = 0 at which the PEelastic is maximum. 2. The earliest instant of time at which the KE of the mass is a maximum and the mass is moving to the right. 3. The earliest instant of time at which the acceleration of the mass is maximum and positive. 4. The earliest instant of time at which the speed of the mass is zero. 18. A. A spring is attached to a post at the top of a 15.0° frictionless ramp. A 2.00 kg mass is attached to the spring and the mass is slowly allowed to stretch the spring to the equilibrium position of the mass-spring system, the spring stretches by 0.400 m See figure. The mass is now pulled an additional 10.0 cm and released. The mass-spring system executes simple harmonic motion. 1. What is the spring constant, k, of the spring. 2. What are the amplitude and period of oscillation of the mass-spring system? B. A solid, uniform cylinder is floating at the interface between water (Dwater = 1.00 × 103 kg/m ) and oil (Doil = 8.24 × 10 kg/m ) with 3/4 of the cylinder in the water region and 3 3 3 1/4 of the cylinder in the oil region. Assume the axis of the cylinder is perfectly vertical. See figure. 1. What is the density of the material out of which the cylinder is made? 2. Assume the upper surface of the oil region si open to the atmosphere (Datm = 1.01 × 10 N/m ) and the oil-water interface is 0.500 m below the 5 2 upper surface of the oil. Also assume the height of the cylinder is 10.0 cm. What is the gauge pressure on the bottom surface of the cylinder? Recall: Pgauge = P – PATM. 19. A. A mass m is attached to a spring and is oscillating on a frictionless horizontal surface (see figure). At the instant the mass is at an amplitude position a second identical mass is carefully placed on top of the original mass. The oscillating system is now the spring and the two identical masses. Relative to the original spring-single mass system, the new spring-2-mass system oscillates with a … In the spaces provided below, enter (I) for increased, (D) for decreased, or (R) remains unchanged, that best completes the above last sentence. 1. amplitude. 2. period. 3. frequency. 4. spring constant. 5. maximum speed. 6. mechanical energy. 7. maximum acceleration. B. Suppose you are asked about the absolute pressure at some depth h below the surface of a liquid. The top surface is exposed to the atmosphere on a sunny day in Salt Lake City. For each statement below in the spaces provided, enter I for increase, D for decrease, or R for remains the same, when accounting for what happens to the absolute pressure at the point you are observing. 1. More liquid is added so now the observation point is farther below the surface. 2. The fluid is now exchanged for a less dense fluid. The observation point is at same h. 3. The experiment is moved to New York City, which is at sea level, on a sunny day. 4. The fluid is now seen to be moving with some speed v past the observation point. 5. The observation point is moved closer to the surface of the liquid. 6. The air above the fluid is removed by a vacuum system. 7. The apparatus is moved to a laboratory on the surface of the moon. 20. A 3.00 kg mass is attached to a spring (k = 52.0 N/m) that is hanging vertically from a fixed support. The mass is moved to a position 0.800 m lower than the unstretched position of the end of the spring. The spring is then released and the mass-spring system executes SHM. Take the 0.800 m of the mass as the reference location for its gravitational PE. A. What is the equilibrium position of the mass-spring system? B. What is the amplitude of the SHM the mass-spring system executes? C. What is the period of the oscillation of this system? D. What is the total mechanical energy of the mass-spring system at the moment the mass is released? E. What are (i) the KE of the mass and (ii) the speed of the mass when the spring is at its equilibrium position? 21. A 38.0 kg block is moving back and forth on a frictionless horizontal surface between two springs. The spring on the right has a force constant kR = 2.50 × 10 N/m. When the block is between the two 3 springs its speed (v) is 1.82 m/s. See figure. A. If the block compresses the left spring to 5.62 cm beyond its uncompressed length, determine the value of kL. B. What is the maximum compression of the right spring when the mass interacts with it? C. What is the total time the spring on the right is compressed during a single event? 22. Two identical containers are connected at the bottom via a tube of negligible volume and a valve which is closed. Both containers are filled initially to the same height of 1.00 m, one with chloroform (DC = 1530 kg/m ) in the left chamber and the other 3 with mercury in the right chamber (DHg = 1.36 × 10 kg/m ). 4 3 Sitting on top of each identical circular container is a massless plate that can slide up or down without friction and without allowing any fluid to leak past. The radius of the circular plate is 12.0 cm. The valve is now opened. A. What volume of mercury drains into the chloroform container? (Note: Vcyl = Br h) 2 B. What mass must be placed on the plate on the chloroform side to force all the mercury, but none of the chloroform, back to the mercury chamber? 23. A 12.0 kg mass M is attached to a cord that is wrapped around a wheel in the shape of a uniform disk of radius r = 12.0 cm and mass m = 10.0 kg. The block starts from rest and accelerates down the frictionless incline with constant acceleration. Assume the disk axle is frictionless. Note: Idisk = 1/2 mr . 2 A. Use energy methods to find the velocity of the block after it has moved 2.00 m down the incline. B. What is the constant acceleration of the block and the angular acceleration of the wheel? C. How many revolutions does the wheel turn for the distance the block travels in (A)? D. If the uniform disk were replaced by a uniform sphere with the same r and m of the disk, would the acceleration of the block attached to the sphere be larger, smaller, or the same as that for the block attached to the disk? Note: Isphere = 2/5 mr . 2 24. A pulley is in the shape of a uniform disk of mass m = 5.00 kg and radius r = 6.40 cm. The pulley can rotate without friction about an axis through the center of mass. A massless cord is wrapped around the pulley and connected to a 1.80 kg mass. The 1.80 kg mass is released from rest and falls 1.50 m. See figure. Note: Idisk = 1/2 mr . 2 A. Use energy methods to determine the speed of the block after falling 1.50 m. B. What is the constant acceleration of the block and the angular acceleration of the wheel? C. How many revolutions does the pulley disk turn for the distance the block travels in (A)? D Suppose the disk were replaced by a uniform sphere with the same r and m of the disk. Would the acceleration of the block attached to the sphere be larger, smaller, or the same as that for the block attached to the the disk? Note: Isphere 2/5 mr . 2 26. A 700.0 N fisherman is walking toward the edge of a 200 N plank as shown. He has placed a can of worms weighing 75.0 N on the left side of the plank as indicated in the drawing. The plank is the horizontal section in the drawing. A. Identify all the forces the plank feels before it begins to tip. Draw a free body diagram. B. As the fisherman nears the point on the plank where it begins to tip, how do the upward forces the supports exert on the plank change. C. How far a distance, as measured from the center of the right support, can he walk before the plank begins to tip? 26. A 75.0 kg sign hangs from a 4.80 m uniform horizontal rod whose mass is 120 kg. The rod is supported by a cable that makes an angle of 53° with the rod. he sign hangs 3.60 m out along the rod. A. What is the tension in the cable? B. What are the forces PPv and PPH exerted by the wall on the left end of the rod? 27. A 1.00 × 104 N great white shark is hanging by a cable attached to a 4.00 m massless rod that can pivot at its base. See figure. A. Determine the tension in the cable supporting the upper end of the rod. See figure. B. Determine the force (a vector quantity) exerted on the base of the rod. Suggestion: Find this force by first evaluating the separate components of the force. See figure. 28. A 6.00 m uniform beam extends horizontally from a hinge fixed on a wall on the left. A cable is attached to the right end of the beam. The cable makes an angle of 30.0° with respect to the horizontal and the right end of the cable is fixed to a wall on the right. At the right end of the cable hangs a 140.0 kg mass. The mass of the beam is 240.0 kg. See figure. A. Find the tension in the cable. B. Find the vertical and horizontal forces the hinge exerts on the left end of the beam. 29 A. The blades of a “Cuisinart” blender when run at the “mix” level, start from rest and reach 2.00 × 103 rpm (revolutions per minute) in 1.60 s. The edges of the blades are 3.10 cm from the center of the circle about which they rotate. 1. What is the angular acceleration of the blades in rad/s2 while they are accelerating? 2. Through how many rotations did the blades travel in that 1.60 s? 3. If the blades have a moment of inertia of 5.00 × 10-5 kg m2, what net torque did the blades feel while accelerating? B. A 7.50 × 10 N 4 shipping crate is hanging by a cable attached to a uniform 1.20 × 104 N steel beam that can pivot at its base. A second cable supports the beam and is attached to a wall. See figure. 1. Determine the tension T in the upper cable. 2. Determine the magnitude of the force exerted on the beam at its base. See drawing. 30. The drawing shows a uniform ladder of length L and weight 220 N. The ladder is sitting at an angle of 30° above the horizontal resting on the corner of a concrete wall at a point that is one-fourth of the way from the end of the ladder. A 640 N construction worker is standing on the ladder one-third of the way up from the end of the ladder which is resting on the ground. Assume the corner of the wall on which the ladder rests exerts only a normal force on the ladder at the point where there is contact. A. What is the magnitude of the normal force the wall exerts on the ladder? B. Find the magnitude of both the normal force the ground exerts on the left end of the ladder and the static frictional force the ground exerts on the left end of the ladder. 31. A. A solid, right circular cylinder (radius = 0.150 m, height = 0.120 m) has a mass m. The cylinder is floating in a tank in the interface between two liquids that do not mix: water on the bottom and oil above. One-third of the cylinder is in the oil layer (Doil = 725 kg/m ) 3 and two-thirds in the water layer (Dwater = 1.00 × 10 kg/m ). See 3 3 drawing. Note: V(circular cylinder) = B r2 h. 1. Find the mass of the cylinder. 2. With the cylinder present, take the thickness of the oil layer to be 0.200 m and the thickness of the water layer to be 0.300 m. What is the gauge pressure at the bottom of the tank? Assume the top of the oil layer is exposed to the atmosphere. B. A block rests on a frictionless horizontal surface and is attached to a spring. When set into simple harmonic motion, the block oscillates back and forth with an angular frequency of T = 7.52 rad/s. The drawing indicates the position of the block when the spring is unstretched. That position is labeled “x = 0 m” in the drawing. The drawing also shows a small bottle whose left edge is located at Xb = 0.0900 m. The block is now pulled to the right, stretching the spring by Xs = 0.0343 m, and is then thrown to the left, i.e., given an initial push to the left. In order for the block to knock over the bottle when it is moving to the right, it must be “thrown” with an initial speed to the left v0. Ignoring the width of the block, what is the minimum value of v0? 32. B. Three objects, a disk (ICM = ½ MR ), a hoop (ICM = MR ), and a hollow ball (ICM = b MR ) all have 2 2 2 the same mass and radius. Each is subject to the same uniform tangential force that causes the object, starting from rest, to rotate with increasing angular speed about an axis through the center of mass for each object. In the case of the hollow ball the tangential force has a moment arm equal to the radius of the ball. In the space below, enter D for disk, H for hoop, and/or B for hollow ball, or same to best answer the question. 1. The object with the largest moment of inertia about the axis through the CM. 2. The object experiencing the greatest net torque. 3. The object with the greatest angular acceleration during the period the force is acting. 4. The object rotating with the smallest angular speed assuming the force has been acting for the same length of time on each object. 33. A. A uniform disk (D), hoop (H), and sphere (S), all with the same mass and radius, can freely rotate about an axis through the center of mass (CM) of each. A massless string is wrapped around each item. The string is used to apply a constant and equal tangential force to each object. See figure. For the statements below, enter D, H, S, none or the same. Assume all objects start from rest at the same instant. 1. The one with the smallest moment of inertia about the shown axis. 2. The object experiencing the largest net torque. 3. The object undergoing the smallest angular acceleration. 4. The object with the largest angular speed after an elapsed time of 5.0 s. 5. The object for which the largest amount of string has unraveled in 5.0 s. 6. The object with the smallest KErot after 5.0 s. 7. The object that undergoes the most rotations in 5.0 s. B. A spherical object is completely immersed in a liquid of density Dliq some distance above the bottom of the vessel. See figure. The upper surface is initially open to the earth’s atmosphere at sea level. Assume the liquid and object are both incompressible. For the items below, indicate whether the object sinks to the bottom (B), rises to the surface (T), or does nothing (N). 1. The vessel is brought to Salt Lake City. 2. Salt is dissolved in the liquid in the same way fresh water is turned into salt water. 3. The top 50 cm3 of the liquid is removed from the vessel. 4. The entire apparatus is transported to the surface of the moon. 5. The volume of the spherical object is increased by heating it without heating the liquid. 6. The spherical object is moved 10 cm farther down in the vessel and released. 7. A mass is placed on the top surface of the liquid in the vessel increasing the pressure at the surface. No fluid leaks. 34. A 2.20 × 103 N uniform beam is attached to an overhead beam as shown in the drawing. A 3.60 × 103 N trunk hangs from an attachment to the beam two-thirds of the way down from the upper connection of the beam to the overhead support. A cable is tied to the lower end of the beam and is also attached to the wall on the right. A. What is the tension in the cable connecting the lower end of the beam to the wall? B. What are magnitude of the vertical and horizontal components of the force the overhead beam exerts on the upper end of the beam at P? 35. A. A 12.0 kg block moves back and forth on a frictionless horizontal surface between two springs. The spring on the right has a force constant k = 825 N/m. When the block arrives at the spring on the right, it compresses that spring 0.180 m from its unstretched position. 1. What is the total mechanical energy of the block and two spring system? 2. With what speed does the block travel between the two springs while not in contact with either spring? 3. Suppose the block, after arriving at the left spring, remains in contact with that spring for a total time of 0.650 s, before separating on its way to the right spring? Using the connection between this 0.650 s and the period of oscillation between the block and the left spring, determine the spring constant of the left spring. B. A turkey baster (see figure) consists of a squeeze bulb attached to a plastic tube. When the bulb is squeezed and released, with the open end of the tube under the surface of the turkey gravy, the gravy rises in the tube to a distance h, as shown in the drawing. It can then be squirted over the turkey. Using Patm = 1.013 × 105 N/m2 for atmospheric pressure and 1.10 × 103 kg/m3 for the density of the gravy, determine the absolute pressure of the air in the bulb with the distance h = 0.160 m. Give answer to three significant digits. 36. A. The pictures below depict three glass vessels, each filled with a liquid. The liquids each have different densities, and DA > DB > DC. In vessel C an unknown block is neutrally buoyant halfway to the bottom and completely submerged. A, B, and/or C, or none are all possible answers. 1. _______ In which vessel(s) would the block sink all the way to the bottom? 2. _______ In which vessel(s) would the largest volume of the block be exposed above the surface of the liquid? 3. _______ In which vessel(s) would the buoyant forces on the block be the same? B. A swinging pendulum (A) and a mass-spring system (B) are built to have identical periods. For the statements below enter either A, B, U (unchanged) to best fit which oscillating system would have the larger period as a result of the change. 1. _______ The mass of the mass-spring system is increased. 2. _______ The mass of the swinging pendulum is increased without altering the location of its center of mass. 3. _______ The spring constant of the mass-spring system is increased. 4. _______ The length of the swinging pendulum system is increased. 5. _______ Both systems are taken to the moon and set oscillating. C. A block of mass m moves back and forth on a frictionless surface between two springs. See drawing. Assume kL > kR. For the statements below enter L for the left spring, R for the right spring, or same as the case may be. 1. _______ The spring that has the maximum compression when m is momentarily at rest. 2. _______ The spring that stores the larger elastic potential energy when maximally compressed. 3. _______ The spring that momentarily stops the block in the least time once the block arrives at the spring. 37. A uniform beam extending at right angles from a wall is used to display an advertising sign for an eatery. The beam is 2.50 m long an weighs 80.0 N. The sign, whose dimensions are 1.00 m by 0.800 m, is uniform, and weighs 200. N, hangs from the beam as shown in the drawing. A cable, attached to the wall of the eatery at a point on the beam where the inside end of the sign is attached to the beam and making an angle of 60.0° with the beam, supports this advertising structure. A. What is the magnitude of the tension in the cable supporting the beam? B. What are the magnitudes of the horizontal and vertical forces the wall exerts on the left end of the beam? 38. A. Examine the picture shown to the right. Initially, before the pump is turned on, the two masses (m1 = 1.00 kg, m2 = 2.75 kg) are held in place. the pressures above and below m1 are Patm = 1.01 × 10 N/m and 5 2 the spring is in its unstretched position. The pump is turned on and the masses are allowed to move. The mass m1 moves without friction inside a cylindrical piston of radius r = 3.85 cm. Once equilibrium is established, by what distance has the spring stretched? Take k = 2.00 × 103 N/m for the spring constant. B. A solid cylinder (radius 0.125 m and height 0.150 m) has a mass of 6.50 kg. The cylinder is floating in water. Oil (Doil = 725 kg/m ) is poured on top of the water until 3 the situation shown in the drawing results. How much of the height (in meters) of the cylinder remains in the water layer?